(1) (Exponents) Simplify the expression (i.e. write with only positive exponents such that x and y occur only once).
(2) (Complex Numbers) Rewrite this expression as a complex number in standard form (i.e. your answer should be in the form a+bi where a and b are real numbers).
(3) (Fractions) Simplify
(4) (Quadratic Equation) Find all the solutions of the equation
(5) (Domain) What is the domain of f?
These values will make the denominator go to zero, which we cannot allow. So, the domain is
(6) (Evaluating a function at a number) Find .
(7) (Evaluating a function at an expression) Find .
(8) (Linear System) Solve the linear system. (Make sure to show all your work!)
x + y + z = 2 x + y + z = 2
-R1+R2 x + 2y - 2z = 1 à y - 3z = -1 à
2R1+R3 -2x - y + 3z = 3 -R2+R3 y + 5z = 7
x + y + z = 2
y - 3z = -1 à z =1 à y - 3(1) = -1 à
8z = 8 y = 2
x+ 2 + 1 = 2
x = -1
Solution is (-1, 2, 1)
(9) (Quadratic Equation) Find all solutions of the equation
This does not factor, so we either need to complete the square or use the quadratic formula to solve this. I will choose the quadratic formula.
a = 2, b = -1, c = -7
(10) (Word Problem) A grocer wants to mix cashews worth $8 per pound with peanuts worth $3 per pound. She wants to obtain a mixture to sell for $4 per pound. How many pounds of peanuts must be used with 5 pounds of cashews?
Peanuts $3 / lb. x lbs.
Cashews $8 / lb. 5 lbs.
Mixture $4 / lb. (5+x) lbs.
Our equation will equate total cost with total cost.
3x + 8(5) = 4(5+x)
3x + 40 = 20 + 4x
-x + 40 = 20
-x = -20
x = 20
à 20 lbs of peanuts must be mixed with 5 lbs. of cashews to get a $4/lb. mixture.
(11) (Rational Equation) Find all solutions of
LCD = (x-1)(x+4)
(12) (Straight Lines) Find the equation of the line that passes through the point
(1,2) and has slope -3.
(13) (Polynomials) Simplify the following polynomial expression. What is its degree and its leading coefficient?
Degree = 3, Leading Coefficient = 2
(14) (Linear System) Solve the system of equations. (Make sure you show all your work.)
You can either use the method of substitution or the method of elimination. I will use elimination.
à à (3, -2)
(15) (Distance) Find the distance between the point (3, 2) and (-1, 4).
(16) (Radical Equation) Find the solution to the equation.
(17) (Division of Polynomials) Perform the division.
à Answer is:
(18) (Word Problem) Joe takes 3 hours to do a job and Fred takes 7 hours to do that same job. Working together, how long will it take them to complete the job?
Let x = number of hours it takes Joe and Fred working together to do the job
LCD = 21x
à So, it takes hours to do the job together.
(19) (Linear Equation) Solve the equation.
(20) (Rational Expressions) Simplify the expression.
LCD = (x + 5)(x - 3)(x – 1)